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International Journal of Greenhouse Gas Control 34 (2015) 39–51

Contents lists available at ScienceDirect

International Journal of Greenhouse Gas Control

j ourna l h o mepage: www.elsev ier .com/ locate / i jggc

arallel simulation of fully-coupled thermal-hydro-mechanicalrocesses in CO2 leakage through fluid-driven fracture zones

hao-Qin Huanga,b, Philip H. Winterfeldb, Yi Xiongb, Yu-Shu Wub, Jun Yaoa,∗

School of Petroleum Engineering, China University of Petroleum (East China), Qingdao, ChinaDepartment of Petroleum Engineering, Colorado School of Mines, Golden, CO, USA

r t i c l e i n f o

rticle history:eceived 15 July 2014eceived in revised form 1 November 2014ccepted 19 December 2014vailable online 19 January 2015

eywords:O2 leakageluid-driven fracturehermal-hydro-mechanical couplingully-coupled simulationarallel computing

a b s t r a c t

The safety of CO2 storage in geological formations relies on the integrity of the caprock. However, theelevated fluid pressure during CO2 injection changes the stress states in the caprock, and may lead toreactivate pre-existing fractures or even fracture the caprock. It is necessary to develop an efficient andpractical monitor technology to detect and identify CO2 leakage pathways. To this end, we should under-stand the transport behavior of CO2 coupled with geomechanical effects during injection. In this work,we first developed an efficient parallel fully-coupled thermal-hydro-mechanical simulator to model CO2

transport in porous media. The numerical model was verified through classical problems with analyti-cal solutions. Then, based on this simulator, we investigated the fluid flow behavior when CO2 leakageoccurs through fluid-driven fracture zones. We proposed an implicit, physics-based model to simulate thefluid-driven fracturing process by using several practical correlations, including fracturing pressure func-tions, porosity/permeability–stress relationships. A set of numerical simulations have been conducted

by considering various scenarios, such as different injection rates, locations and distributions of fracturezones, and initial fracture permeability. The results show that there are several characteristics can beused to detect CO2 leakage pathways, and it is possible to develop an advanced inverse modeling andmonitoring technology to identify leakage locations, times and rates using measured pressure data ofpermanent downhole gauges and our simulator.

. Introduction

To address the increasing concerns regarding greenhouse gasmission and its impact on global climate, CO2 geologic seques-ration is considered to be among the most promising, viablepproaches for near-term implementation (Bolster, 2014; Huppertnd Neufeld, 2014). Carbon dioxide can be sequestered in sev-ral types of geological media including deep saline aquifers,epleted oil and gas reservoirs, and coal beds. To achieve signif-

cant reduction of atmospheric emissions, large amounts of CO2eed to be injected into geologic storage reservoirs, leading to pres-ure buildup and significant changes in formation stress. CO2 isupercritical and buoyant relative to groundwater under typicalubsurface conditions. If vertical pathways are available or cre-

ted through elevated pressure reactivating fractures or faults, CO2ill tend to flow upward and escape and, depending on geologic

∗ Corresponding author. Tel.: +1 720 278 3875.E-mail addresses: huangzhqin@upc.edu.cn, huangzhqin@gmail.com

Z.-Q. Huang), rcogfr upc@126.com (J. Yao).

ttp://dx.doi.org/10.1016/j.ijggc.2014.12.012750-5836/© 2014 Elsevier Ltd. All rights reserved.

© 2014 Elsevier Ltd. All rights reserved.

conditions, may reach drinking water aquifers or even the landsurface (Rinaldi et al., 2014).

Physical testing methods for detecting CO2 leakage includesurface to borehole seismic imaging, cross-well seismic, cross-well electromagnetic, well logs, and tracer injection tests (Benson,2006). These methods are useful in detecting existing conduc-tive fractures or faults in reservoirs/caprocks (Lee et al., 2012; Luoet al., 2010; Sminchak et al., 2002), but they cannot detect leakagethrough induced fractures during CO2 injection and the long-termstorage afterwards. A recent study (Zoback et al., 2012) has shownthat micro seismic events do not correlate well with “fracturing” inshale gas reservoirs, because slow fault slip does not generate highfrequency seismic waves that can be detected by current seismictechnology.

Analytical models have also been used to identify CO2 leakageand specify leakage parameters, such as location, orientation andtransmissibility (Sun et al., 2013; Zeidouni, 2012; Zeidouni et al.,2011a,b; Zhou et al., 2008). In these models, pressure buildup

or drop tests were carried out to determine the CO2 and brinedisplacement in a deep saline aquifer. However, these models wereused under simplified conditions, for example, a single injectionwell and/or single monitoring well in a homogenous reservoir,

40 Z.-Q. Huang et al. / International Journal of Greenhouse Gas Control 34 (2015) 39–51

Nomenclature

Aij cross area between grid i and j (m2)a coefficient in porosity-stress correlationb aperture of fractures (m)Ci constants in fractures’ permeability–aperture cor-

relation, i = 1,2c coefficient in permeability–stress correlationCR heat conductivity of rock gains (W/K/m)dij distance between grid i and j (m)M� accumulation terms of the components �F� flux terms of the components � along boundaries or

cross sectionsf body force (Pa/m)G shear modulus (Pa)g gravity acceleration constant (m/s2)h specific enthalpy (J/kg)I identity matrixK bulk modulus (Pa)Kh lateral stress coefficientk absolute permeability (m2)k0 permeability at zero effective stress (m2)kf fracture permeability (m2)kf0 fracture permeability at zero effective stress (m2)krl relative permeability of fluid phase lNk numbers of mass componentsn the unit normal vector of boundary �p fluid pressure (Pa)pc capillary pressure (Pa)pc0 entry capillary pressure (Pa)pf hydraulic fracturing pressure (Pa)q� sources or sinks terms of the components �R equation residualSl saturation of fluid phase lT temperature (K or ◦C)T0 reference temperature (K or ◦C)t time (s)u displacement vector (m)V the domain volume (m3)v the Darcy velocity (m/s)X�

lmass fraction of component � in fluid phase l

Greek letters˛ Biot’s coefficient

linear thermal expansion coefficient (◦C−1)� porosity�0 porosity at zero effective stress�r porosity at high effective stress� thermal conductivity (W/K/m)�S Lame’s constant (Pa)ε strain tensorεv volumetric strain� density (kg/m3)v Poisson’s ratio� stress tensor (Pa)�h horizontal stress (Pa)�m mean stress (Pa)�v vertical stress (Pa)� ′ effective stress (Pa)� rock grain density (kg/m3)

R

� boundary of domain

Subscripts and superscriptsk the index for the componentsl fluid phases

Fig. 1. Schematic of CO2 injection in the presence of fractures within the caprocklayer.

and CO2 phase properties were simplified as well. The ana-lytical methods have several limitations and they are in generalunable to consider the complex phase behavior during CO2injection and realistic reservoir heterogeneity.

In comparison, numerical simulations are able to accountfor CO2 multiphase flow and complicated phase behavior, diffu-sion/dispersion, geomechanics (Hu et al., 2013; Winterfeld andWu, 2012), and chemical reactions (Zhang et al., 2012) duringCO2 injection and storage. So numerical simulation tools are moresuitable for quantifying CO2 leakage locations and rates under real-istic field conditions (Pruess and Nordbotten, 2011; Pruess et al.,2003; Rutqvist and Tsang, 2002; Rutqvist et al., 2002; Siriwardaneet al., 2013). To predict potential CO2 leakage pathways and quan-tify leakage rates in storage geological formations, the effect ofgeomechanics and rock deformation must be included in the modelformulation. This is an active research area and several simulatorshave been used extensively for CO2 sequestration modeling, suchas the TOUGH2 family of codes (Pruess et al., 1999; Zhang et al.,2008), GEM (Kumar et al., 2008; Siriwardane et al., 2013), DuMux(Class et al., 2009), and OpenGeoSys (Hou et al., 2012).

Physically, CO2 leakage from a storage formation will occurwhen the reservoir pressure is high enough to cause mechanicalfailure in caprocks or in the wellbore (as depicted in Fig. 1). In aCO2 geological storage reservoir with large storage capacity, theincrease in pressure should be gradual and may last for years dur-ing continuous CO2 injection. This is very different from a hydraulicfracturing operation, in which a small-volume packed wellbore sec-tion is subject to a high injection rate of fracturing fluid in a veryshort period of time in order to fracture the rock. Depending onfield geological conditions, high pressure buildup in CO2 storagesystems is needed to fracture caprocks or fault zones, and CO2 isvery likely in a liquid or supercritical phase at that high pressure.CO2 leakage, if occurring, will lead to some drop in pressure thatwill propagate rapidly in a pressurized, liquid-filled reservoir. Thechanges in reservoir pressure associated with the occurrence ofCO2 leaking will be “seen” by multiple observation wells equippedwith downhole pressure sensors. And the collected data can be ana-lyzed using advanced inverse modeling and optimization schemesto identify leakage that is likely to be occurring. In comparison, thesame pressure signals or leakage through fracture zones may notbe strong enough to be detected by geophysical or remote sensingtechnologies.

Therefore, there is a need to understand how the flow andpressure transients are affected by CO2 multiphase flow and com-plicated phase behavior, coupled with geomechanical effects. Theobjectives of this paper are to investigate fluid flow behaviorwhen CO2 leakage occurs through caprock fractures or geome-chanically activated faults by using our parallel fully-implicit and

fully-coupled simulator. In this work, we don’t focus on explicitmodeling of the dynamic propagation of the caprock fractures.Although the fracture propagating process is important to geome-chanics and several modeling approaches have been developed

l of Gr

(RibAl(rbf

mC(uloac

2

2

aQDFtitttt

atf

(

M

r

M

F

we

�

d

F

R�i

(xt+�t

)

Z.-Q. Huang et al. / International Journa

Lecampion, 2009; Pan et al., 2013; Peirce and Detournay, 2008;ichardson et al., 2011; Xu and Wong, 2010), the fact that numer-

cally simulating the fracture propagation is widely known toe difficult, especially for coupling with large-scale porous flow.lternatively, we use an implicit, physics-based model to simu-

ate such dynamic process by using several practical correlationse.g. fracturing pressure functions, porosity/permeability–stresselationships, etc.). The pressure signatures and changes in flowehavior are investigated to explore their use in detecting caprockractures, which are our concerns.

The paper is organized as follows. We first outline the basicathematical and numerical models of our simulator, named THM-

O2, which is a parallel fully-coupled thermal-hydro-mechanicalTHM) simulator. Then, the fluid-driven fracture zone is modeled bysing a physics-based and practical approach, including the corre-

ations of hydraulic properties. Thereafter, the implement schemef the codes is explained, and its validity is verified through twonalytical solutions. Finally, several CO2 leakage simulations areonducted in various geomechanical and flow conditions.

. Mathematical and numerical model

.1. Multiphase fluid and heat flow model

Our simulator is based on the general mass and energy bal-nce equations (Pruess et al., 1999; Rutqvist et al., 2002; Wu andin, 2009). Fluid flow is described by a multiphase extension ofarcy’s law and diffusive mass transport is considered in all phases.or the energy balance equation, heat transport occurs by conduc-ion and convection, with sensible as well as latent heat effectsncluded. The description of thermodynamic conditions is based onhe assumption of local equilibrium of all phases. Fluid and forma-ion parameters can be arbitrary nonlinear functions of the primaryhermodynamic variables. The mass and energy conservation equa-ions in integral form are:

∂∂t

∫V

M�dV =∫

�

F� × nd� +∫

V

q�dV (1)

The integration is over an arbitrary domain V with closed bound-ry � . Here, M� in the accumulation term, with � = 1, . . ., N� , labelinghe mass components (air, water, CO2, solutes, . . .), and � = N� + 1or the energy “component”.

The mass accumulation term is a sum over the fluid phases l=gas, liquid, NAPL):

� = �∑

l

Sl�lX�l (2)

The energy accumulation term accounts for fluid phases andock:

� = (1 − �)�RCRT + �∑

l

Sl�l�l, k = Nk + 1 (3)

The mass flux of component � is a sum over fluid phase l:

� =∑

l

�lXkl �l (4)

here the Darcy velocity �l of phase l is given by the multiphasextension of Darcy’s law:

l = −kkrl

l(∇pl − �lg) (5)

For the energy conservation equation, heat flux includes con-

uctive and convective terms:� = −�∇T +

∑l

�lhl�l, � = N� + 1 (6)

eenhouse Gas Control 34 (2015) 39–51 41

The definitions of all symbols used above can be found in theNomenclature.

2.2. Geomechanical model

In this work, we fully couple geomechanics to fluid and heatflow. Rock mass is assumed to be a thermal-poroelastic materialand obeys a generalized version of Hooke’s law (McTigue, 1986):

� −(

˛p + 3ˇK (T − T0))

I = 2Gε + �SεVI (7)

Relating stresses and displacements are combined to yield anequation for mean stress, which is a function of pore pressure andtemperature. The mean stress is an additional primary variable tomultiphase flow system. Under the assumption of linear elasticitywith small strains for a thermo-poroelastic system, the equationsfor the stresses in terms of the strains can be expressed as fol-lows (Jaeger et al., 2009). The trace of the general Hooke’s law fora thermo-poroelastic medium is:

KεV = �m − ˛p − 3ˇK (T − T0) (8)

The additional geomechanical equations, namely the equationof stress equilibrium (momentum):

∇ · � + f = 0 (9)

The strain tensor definition ε =(∇u + (∇u)T

)/2, is combined

with Eq. (7) yield to the thermo-poroelastic Navier equation:

∇ (˛p + 3ˇK (T − T0)

)+ (�S + G) ∇ (∇ · u) + G∇2u + f = 0 (10)

Taking the divergence of Eq. (10), and combining with Eq. (8)yields the governing equation for mean stress:

3 (1 − v)1 + v

∇2�m + ∇ · f − 2 (1 − 2v)1 + v

(˛∇2p + 3ˇK∇2T

)= 0 (11)

Note that the divergence of the displacement vector is the volu-metric strain. In this paper, only fully elastic problem is considered.Furthermore, the boundary conditions for Eq. (11) are mean stressspecified on the boundary, which will be described in Section 2.3.

2.3. Numerical discretization and implementation

In THM-CO2 simulator, the mass, energy, and momentumbalance equations are discretized in space using the integral finite-difference method (Pruess et al., 1999; Wu and Qin, 2009). Thesimulation domain is subdivided into a structured or unstructuredmesh. Time derivatives are evaluated using the standard first-orderapproximation, and flux and accumulation terms are evaluatedfully implicitly. As a result, the set of coupled nonlinear mass andenergy conservation equations can be written in residual form as:

R�i

(xt+�t

)= M�

i

(xt+�t

)− M�

i

(xt

)

− �t

Vi

⎛⎝∑

j

AijF�ij

(xt+�t

)+ Viq

�,t+�ti

⎞⎠ = 0 (12)

Similar to the mass and energy equations, the finite differenceapproximation for Eq. (11) in residual form is (Winterfeld and Wu,2014):

=∑

j

(3 (1 − v)

1 + v�mj − �mi

dij− 2˛ (1 − 2v)

1 + vpj − pi

dij− 2ˇE

1 + vTj − Ti

dij+ f · n

)ij

Aij = 0

(13)

42 Z.-Q. Huang et al. / International Journal of Gr

gdp

fbucewv

−

wicFpts(

apEg(mdp(g

Tsang, 2002):

Fig. 2. Numerical implement architecture and flow chat.

Here, � = N� + 2 represents the stress “component”.Strictly speaking, grid block geometry is no longer fixed due to

eomechanical effects. However, under the assumption of smalleformations, we can neglect this geometrical variation. This isractical for accuracy required for field cases.

The model solves for four primary variables (pressure, air massraction/gas saturation, temperature, and mean stress) for each gridlock. The primary variables pressure, air mass fraction/gas sat-ration and temperature are aligned with the mass and energyonservation Eq. (12). Mean stress is aligned with Eq. (13). Thesequations are solved by the Newton–Raphson method, Eq. (14),hich iterates until the residuals are reduced below preset con-

ergence criteria:

∑i

∂R�i

(xt+�t

)∂xi

∣∣∣∣∣n

(xn+1 − xn) = R�i

(xt+�t

n

)(14)

here n denotes the iterative step during one time step. THM-CO2s implemented in parallel code and with MPI used for communi-ations between processors. A flow chart for the code is shown inig. 2. All data input and output are carried out through the masterrocessor. The most time-consuming computations (assemblinghe Jacobian matrix, updating thermo physical parameters, andolving linear equation systems) are distributed to all processorsWinterfeld and Wu, 2014).

In the THM-CO2 code, domains are partitioned using the METISnd ParMETIS packages (Karypis and Kumar, 1998a,b) with threeartitioning algorithm options, K-Way, VK-Way, and Recursive.ach processor computes Jacobian matrix elements for its ownrid blocks. Exchange of information between processors uses MPImessage passing interface) and allows calculation of Jacobian

atrix elements associated with inter-block connections acrossomain partition boundaries. The Jacobian matrix is solved in

arallel using an iterative linear solver from the Aztec packageTuminaro et al., 1999). Aztec solver options include conjugateradient and generalized minimum residual, among others. The

eenhouse Gas Control 34 (2015) 39–51

detailed descriptions of the parallel scheme can be found in ourprevious works (Wang. et al., 2014; Winterfeld and Wu, 2014).

3. Fluid-driven fracture modeling

Caprock acts as a sealing agent with regard to carbon dioxidestorage and any fracturing in it may lead to CO2 leakage from thesaline aquifer. There are usually some dormant faults or micro frac-tures (such as joints) in shale caprock, which will be activated orhydraulic fractured due to the buildup of fluid pressure during theCO2 injection. Recently, Gor et al. (2013) developed an analyticalmodel to predict fluid-driven fracture propagation, and applied themodel to the Krechba aquifer in Salah, Algeria (Rutqvist et al., 2010).Their results show that initially the fracture propagation is veryfast: 100 m within less than a minute after initiation. Therefore,we will model such a fracturing process by using a physics-based,practical method rather than explicitly simulating of fracture prop-agation.

There are two steps in our method. In the first step, an empiri-cal criterion will be used to predict the fracturing pressure, whichdetermines whether the fractures are activated or initialized in gridblocks. In the second, the hydraulic properties, such as porosity andpermeability, of these fracturing grid blocks are calculated usingstress-dependent correlations.

3.1. Fracturing pressure

There is much experimental and analytical research has beenconducted in the past several decades for determining the frac-turing pressure. Ghanbari and Shams Rad (2013) summarized thepublished fracturing equations and developed a new empirical cri-terion. They compare various published equations, which are listedin Table 1. In this work, the equation developed by Ghanbari andShams Rad (2013) is used.

In our fully-coupled simulator, only the mean stress and the vol-ume strain are calculated. So, an additional relationship is neededto evaluate the horizontal stress �h. For the in-situ state of stressin the subsurface, the vertical stress and horizontal stress are usu-ally related by the lateral stress coefficient Kh, i.e. �h = Kh�v (Jaegeret al., 2009). Because the fluid pressure slowly increases during theCO2 injection period, fluid has time to diffuse into the rock andconsequently the rock deforms slowly and uniformly. Therefore,the variation of the lateral stress coefficient would be small, sowe assume it is constant. Based on this, we obtain the horizontalconfining stress as:

�h = 3Kh

2Kh + 1�m, Kh ∈ (0, 1) (15)

3.2. Correlations of hydraulic properties

In the second step, the hydromechanical rock properties are rep-resented by porosity-stress and permeability–stress relationships.For grid blocks without hydraulic fractures, the matrix porosity, �,is related to the mean effective stress as (Rutqvist and Tsang, 2002):

� = �r + (�0 − �r) exp(

a� ′m

)(16)

And the corresponding permeability is correlated to the poros-ity according to the following exponential function (Rutqvist and

k = k0 exp(

c�

�0 − 1

)(17)

Z.-Q. Huang et al. / International Journal of Greenhouse Gas Control 34 (2015) 39–51 43

Table 1The summary of the hydraulic fracturing pressure equations.

The researchers The equations* m n/pm

Jaworski et al. (1981) pf = m�h + �ta – –Fukushima (1986) pf = �min + qu – –Mori and Tamura (1987) pf = m�c 1.3–1.6 –Panah and Yanagisawa (1989) pf = (m�3 − n�3) (1 + sin (�u)) + Cu cos (�u) 1.5 0.5Satoh and Yamaguchi (2008) pf = (m�3 + pm) 1.18–1.82 −14–34 (kPa)Ghanbari and Shams Rad (2013) pf = m�h + pm 1–1.2 20–40 (kPa)

* Please see the definitions of coefficients in corresponding literatures.

Fig. 3. Schematic relationships among axial strain εi , volumetric strain εv and per-mit

p

p

prbSbtrfo

smitItidtte

eability k for fractured rock, and the subscript i denotes the ith-direction. (Fornterpretation of the references to color in this figure legend, the reader is referredo the web version of this article.)

In addition, permeability and porosity are used to scale capillaryressure:

c = pc0

√�0/k0√�/k

(18)

For fractured grid blocks, little work has been done to correlateorosity/permeability to stress/strain. Although the stress–strainelationships and rock failure mechanisms have been investigatedy many researchers (Heiland, 2003; Martin and Chandler, 1994;hiping et al., 1994; Zhu and Wong, 1997), little attention haseen paid to the permeability–stress or strain relationships of frac-ured rocks. Based on experimental data, Zhang et al. (2007) haveeported that the changes of permeability and volumetric strainollow a similar trend shown in Fig. 3, which agrees with the workf Schulze et al. (2001).

Fig. 3 shows that the behavior of permeability and volumetrictrain with axial strain εi exhibits two different stages. Stage I com-ences from the origin until the hydraulic fracture pressure level

s reached, during which the existing fractures are closed due tohe rock contraction, and permeability decreases gradually. StageI, after the fracturing pressure level is exceeded, corresponds tohe initiation of new fractures, which induces a dramatic increasen permeability and volumetric dilation. Meanwhile two different

eformation regions are illustrated in Fig. 3, the elastic- and plas-ic region. The changes of permeability and volumetric strain inhe elastic deformation region can also be divided into two differ-nt sub regions, sub region 1 and 2. In sub region 1, permeability

Fig. 4. Schematic relationships between permeability and volumetric strain.

and volumetric strain are decreasing and in sub region 2, they areincreasing. As aforementioned, we assume rock is elastic medium,so we simplify the model and keep permeability and volumetricstrain constant in Fig. 3 by the blue and red dash lines.

The above indicates that permeability and volumetric strain (ormean stress) are related to each other. In stage I, before fractur-ing initializing, all the fractures are closed, so the permeability-and porosity–stress correlations are those for matrix, i.e., Eqs. (16)and (17). For stage II, a hypothetical correlation curve is shownin Fig. 4, and can be obtained from lab experiments or field testresults. The experimental results of Zhang et al. (2007) also haveshown that the cubic dependence of permeability on fracture aper-ture is valid for a fractured medium and subjected to stresses, so weuse the following relationship between permeability and fractureaperture:

kf = kf,0C1

(1 + �b

C2

)3

(19)

We will use Eq. (19) to evaluate the porosity changes for stageII, because stress-induced changes in hydraulic properties areexpected to be much greater in compliant rock fractures than inthe stiffer matrix (Rutqvist et al., 2002).

4. Numerical implementation and verification

4.1. 1D Consolidation problem

The consolidation problem, in which a fluid-saturated porousmedium is subjected to an instantaneously applied normal load onits upper surface, is one of the most important problems in rockand soil mechanics. Here, a 1D case is simulated and compared tothe analytical solution (Jaeger et al., 2009), as depicted in Fig. 5. We

simulated this problem in two steps.

In the first step, a load is imposed to produce the pore pres-sure increase, which is undrained process. We started from aninitial state where pore pressures and mean stress were initialized

44 Z.-Q. Huang et al. / International Journal of Greenhouse Gas Control 34 (2015) 39–51

Fig. 5. Schematic of evolution of 1D consolidation problem.

Table 2Input data for 1D consolidation problem.

Parameters Value Unit

Porosity 0.2 –Permeability 1.0 × 10−13 m2

Young’s modulus 8.0 GPaPoisson’s ratio 0.2 –Biot’s coefficient 0.2 –Water compressibility 4.4 × 10−10 1/Pa

aspiictumainttm

Ft

Water viscosity 0.89 mPa·s

t 3.0 MPa and 5.0 MPa, respectively. Then, the additional verticaltress of 3.0 MPa was imposed at the column top that induced a poreressure increase in the column. In the second step, fluid drainage

s simulated. We set the pore pressure at the column top to thenitial pore pressure (3.0 MPa). We also set the mean stress at theolumn top to that calculated from the equilibrated system. Fluidhen drained out of the column top as the pore pressure in the col-mn returned to the initial value. The dimensions of the simulatedodel is 1 m × 1 m × 100 m (x × y × z), and the grid size is 1 m, 1 m,

nd 0.25 m in x, y, z directions respectively. The detailed input datas listed in Table 2. The comparison of pore pressure between ourumerical simulations and analytical solutions in Fig. 6 indicateshat our numerical results produce essentially the same answerso analytical models, which verifies the validity of our numerical

odel and approach.

-100.0

-80 .0

-60 .0

-40 .0

-20.0

0.0

3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7

Dep

th (m

)

Pore pressure (MPa)

Numerical simulatio n

Analytical solution

1000 s

10000 s

4000 s

2000 s

ig. 6. Comparison of pore pressure between numerical results and analytical solu-ions.

Fig. 7. Schematic of 2D Mandel’s problem.

4.2. 2D Mandel’s problem

Next, we consider the original two-dimensional Mandel prob-lem, which is depicted as Fig. 7. A constant compressive force isapplied to the top and bottom of a water-filled poroelastic mate-rial, inducing an instantaneous uniform pore pressure increase andcompression. The lateral boundary surfaces perpendicular to thex-direction are at the ambient pressure and are traction free. Thepore pressure near the surfaces will decrease due to drainage. Thematerial there becomes less stiff and an additional load will transferto the center, resulting in a further increase in center pore pressurethat reaches a maximum and then declines. This phenomenon iscalled the Mandel–Cryer effect (Cryer, 1963; Mandel, 1953), andAbousleiman et al. presented an analytical solution to the aboveproblem that we compare our simulated results to Abousleimanet al. (1996).

We simulated the Mandel–Cryer effect problem for a 1000 m

square domain that was subdivided into a uniform 200 × 200grids. The initial pore pressure and mean stress were 0.1 MPa,the applied mean stress was 5.0 MPa, the equilibrium pore pres-sure was 2.179 MPa. The system drained for 50,000 s. Table 3 gives

Table 3Rock properties for Mandel problem.

Input parameters Value Unit

Porosity 0.094 –Permeability 1.0 × 10−13 m2

Young’s modulus 5.0 GPaPoisson’s ratio 0.25 –Biot’s coefficient 1.0 –Pore compressibility 0 –

Z.-Q. Huang et al. / International Journal of Greenhouse Gas Control 34 (2015) 39–51 45

Table 4Rock properties for CO2 leakage simulation model.

Parameters Overburden Aquifer Caprock Saline Underburden

Zero stress porosity, �0 0.01 0.1 0.01 0.1 0.01Residual porosity, �r 0.0904 0.094 0.0094 0.094 0.0094Zero stress permeability, k (m2) 4.0 × 10−15 1.0 × 10−13 4.0 × 10−19 1.0 × 10−13 4.0 × 10−18

Young’s modulus, E (GPa) 5.0 5.0 5.0 5.0 5.0Poisson’s ratio, v 0.25 0.25 0.25 0.25 0.25Biot’s coefficient, 1.0 1.0 1.0 1.0 1.0

Saturated rock density, �S

(kg/m3

)2260 2260 2260 2260 2260

Corey’s irreducible gas saturation 0.05 0.05 0.05 0.05 0.05Corey’s irreducible liquid saturation 0.3 0.3

van Genuchten function exponent, m 0.457 0.457

Entry capillary pressure, pc0 (Pa) 1.96 × 106 1.96 × 1

0.5

1.0

1.5

2.0

2.5

0.0 1.0 2.0 3.0 4.0

Pore

pre

ssur

e (M

Pa)

4

Numerical simulatio nAnalytical solution

tcsaw

5

5

efttiw1

Time (10 s)

Fig. 8. Pore pressure at the center of domain.

he material properties used in this simulation. Fig. 8 shows theomparison of pressure at the center of the domain between theimulation and the analytical solution. The simulated pressure has

peak and shows excellent agreement with the analytical solution,hich lends creditability to our computational approach again.

. CO2 leakage simulation and flow behavior analysis

.1. Fundamental computational model

As shown in Fig. 9, a multi-layered geologic profile is consid-red in this study with a pre-existing fractured zone or dormantractures in the caprock, which may be activated during fluid injec-ion. There are five geologic layers: the upper overburden strata,

he aquifer layer, the shale caprock, the saline layer where CO2njection is planned, and the underburden layer. A vertical injection

ell is placed in the center of the simulation model at a depth of495 m, where the CO2 is at a temperature and pressure for it to be a

Fig. 9. Geometry model for CO

0.3 0.3 0.30.457 0.457 0.457

05 3.125 × 107 1.96 × 105 3.125 × 107

supercritical fluid. The material properties for each layers are givenin Table 4.

Primary variables are initialized at the start of a simulation.In this study, it is desirable for the simulation initialization to behydrostatically stable such that if the system were isolated, theprimary variables would not change over time. In this hydrostaticstability calculation, the temperature is assumed to be 10 ◦C on theground surface and 85 ◦C at 3000 m depth, resulting in a temper-ature gradient of 25 ◦C/km. The pressure at the ground surface isassumed to be atmospheric (0.1 MPa) and, after the steady statecalculation, a pressure of 30 MPa is obtained at the bottom of themodel. The initial stress is assumed to be isotropic and has a depthgradient corresponding to the acceleration of gravity (9.81 m/s2)multiplied by the rock density (2260 kg/m3). The initial porosityand permeability are calculated using the initial stress field andEqs. (16) and (17). The relative permeability and capillary pressureuse Corey’s function and van Genuchten’s function respectively(Rutqvist and Tsang, 2002).

5.2. Influence of a pre-existing fractured zone

In this section, we show the results of CO2 injection modelingin the presence of a fractured zone. Based on the results of thehydrostatic calculation, the initial temperature and pressure at theinjection point are 47.5 ◦C and 15 MPa, respectively, and injectedCO2 is a supercritical fluid. Compressed CO2 is injected at a constantrate of 0.05 kg/s. First, we investigate the influence of a fracturedzone in the caprock. A vertical narrow permeable zone with 10 mwidth was included in the caprock at 300 m from the injectionsource (i.e. at x = 4305 m). The model mesh is constructed with arefined grid in the aquifer, caprock, and saline layers and aroundwell where significant gradients may occur. The x- and z-direction

grid block thickness are shown in Table 5.

For simplicity, material properties of the pre-existing fracturedzone are those of the saline layer. In the numerical simulation, thegrid blocks located on the outer boundaries remain at hydrostatic

2 injection simulation.

46 Z.-Q. Huang et al. / International Journal of Greenhouse Gas Control 34 (2015) 39–51

Table 5The grid block numbers and thickness.

Direction Grid numbers and thickness

x Numbers 10 10 10 101 10 10 10

pCudasardewd

5

iwb

Thickness (m) 200 100

z Numbers 10 20

Thickness (m) 50 20

ressure except the bottom boundary. Fig. 10a shows the spread ofO2 plume in the reservoir with and without the presence of a sim-lated fractured zone at the end of one year injection period. Theifference between their pressure profiles can be found in Fig. 10b,nd CO2 remains as a supercritical fluid in aquifer layer. Fig. 10chows the volumetric strain caused by the CO2 injection in thebsence and presence of a fractured zone. Although the volumet-ic strain profiles are changed greatly, computed ground surfaceeformations computed were relatively smaller. By further consid-ring the heterogeneity of formations, their displacement patternsould be more complicated, and may not be strong enough to beetected by geophysical or remote sensing technologies.

.3. Modeling of fluid-driven fracturing during CO2 injection

In this section, we show the results of CO2 injection model-ng in the presence of a potential fluid-driven fracturing zone,

hich includes dormant fault or micro fractures near the interfaceetween the caprock and saline layers. The initial and boundary

Fig. 10. Comparison of simulation results between computational models in th

50 10 50 100 20020 10 30 10 2610 10 10 20 50

conditions are the same as in Section 5.2. To calculate fracturingpressure, we use the coefficient m = 1.08, pm = 40 kPa, and the lateralstress coefficient Kh = 0.3. A vertical potential hydraulic fracturingzone with 10 m width was included in the caprock at 300 m from theinjection source (i.e. at x = 4305 m). The model mesh is constructedwith a refined grid in the aquifer, caprock, and saline layers, andaround well as shown in Table 5. The permeability–stress correla-tion in Stage II is given as follows based on the model presented byWalsh (1981) and National-Research-Council (US), 1996.

kf = kf 0

(C ln

�f 0

�f − p

)3

(20)

where kf is the permeability of hydraulic fractured zone, kf0 is theinitial permeability of hydraulic fractured zone at Stage II as shownin Fig. 4, �f is the normal stress on the fracture zone, �f0 is the

reference state at the beginning of Stage II, and C is a constant whichis determined by the initial reference state.

First, we investigate the influence of different injection rateson flow behaviors. Compressed CO2 is injected at four different

e absence and presence of a fractured zone after 10-years CO2 injection.

Z.-Q. Huang et al. / International Journal of Greenhouse Gas Control 34 (2015) 39–51 47

n diffe

ctbtb1kc

ttdit((

ist3dMSzCtc

enable us to identify an existing fractured zone which may be acti-vated or newly created.

0

250

500

750

1000

1250

0 400 800 1200 1600 2000

Pres

sure

incr

ease

(kPa

)

Pre-existing fracture zoneHydraulic fr actu ring zoneNo frac ture zone

initial fracturing: after 102 da ys

Fig. 11. Comparison of simulation results betwee

onstant rates of 0.01 kg/s, 0.03 kg/s, 0.05 kg/s and 0.07 kg/s. Inhe numerical simulation, the grid blocks located on the outeroundaries remain at hydrostatic pressure except those on the bot-om boundary. Fig. 11 shows the comparison of simulation resultsetween injection rate 0.03 kg/s and injection rate 0.05 kg/s after0-years CO2 injection. Here, the initial fracturing permeabilityf0 = 0.1 mD (10−13 m2). All the simulation results are similar to thease with a pre-existing fractured zone.

In order to investigate the influence of the fluid-driven frac-ure process on the pressure response, we assume that there arewo permanent downhole gauges (PDG) for continuous pressureata collection in the aquifer and saline layers. The PDG technology

s relatively mature and has been used in the petroleum indus-ry for decades (Horne, 2007). Two gauges are located at positions4005 m, −905 m) (Monitoring Point 1) and (4005 m, −1495 m)Monitoring Point 2), respectively.

Fig. 12 shows the comparison of pressure increase at the Mon-toring Point 1 in the aquifer layer between different modelingcenarios. For the modeling scenario without any fractured zones,he pressure changes are small and the maximum changes is5 kPa. However, the pressure increases in the initial stage and thenecreases to the hydrostatic pressure. This can be explained by theandel–Cryer effect due to consolidation, which has discussed in

ection 4.2. For the modeling scenario with a pre-existing fractured

one, the pore pressure increases gradually from the beginning ofO2 injections. Although a similar phenomenon can be found inhe modeling scenario with a hydraulic fracturing zone, a distincthange in the pressure signature can be seen in Fig. 12. Before

rent injection rates after 10-years CO2 injection.

the zone was fractured or activated, the corresponding pressureresponse should be same as the case without any fractures. In thiscase, the initial hydraulic fracturing took place after 102 days. This

Time (days)

Fig. 12. Pressure changes in the Monitoring Point 1 with different modeling scenar-ios and injection rate 0.05 kg/s.

48 Z.-Q. Huang et al. / International Journal of Greenhouse Gas Control 34 (2015) 39–51

0.0E+0 0

3.0E-05

6.0E-05

9.0E-05

1.2E-04

1.5E-04

0

300

600

900

1200

1500

1800

0 400 800 1200 1600 2000

Flux

(m3 /s

)

Pres

sure

incr

ease

(kPa

)

Time (days)

monitoring point 1: pressuremonito ring point 2: press ureupper grid: fluxbottom grid: flux

Ft

flPtiaisMadcte

cpzcWtcisi(la

ptfrf2F

5

frtaa

(a) the chang es of pressu re and satura tion duri ng CO2 injectio n

(b) local mag nifica tio n of the pressure drop stage

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0

260

520

780

1040

1300

0 500 1000 1500 2000

Gas

satu

ratio

n

Pres

sure

incr

ease

(kPa

)

Times (da ys)

pressure in creaseupper grid: gas saturationbottom grid : gas saturat ion

0.0

0.1

0.2

0.3

0.4

500

550

600

650

700

500 550 600 650 700

Gas

satu

ratio

n

Pres

sure

incr

ease

(kPa

)

Times (da ys)

pressure in creaseupper grid: gas saturatio nbottom grid : gas saturat ion

Fig. 14. The pore pressure changes at the Monitoring Point 1 and gas saturationchanges of the upper and bottom grids in the hydraulic fracturing zone during CO2

injection.

0

500

1000

1500

2000

0 400 800 1200 1600 2000

Pres

sure

incr

ease

(kPa

)

Time (days)

injection rate: 0.07 kg/ sinjection rate: 0.05 kg/ sinjection rate: 0.03 kg/ sinjection rate: 0.01 kg/ s

ig. 13. The pore pressure changes at the monitoring points and fluxes changes ofhe upper and bottom grids in the fluid-driven fracturing zone during CO2 injection.

As shown in Fig. 13, a strong correlation between the leakageuxes from the fractured zone and pore pressures at Monitoringoints can also be observed. At the beginning, the permeability ofhe fluid-driven fracturing zone is the same as that of the surround-ng caprock grid blocks due to the closure of the micro fracturesnd dormant faults. With the pore pressure increasing during CO2njection, the effective stress is reduced in fractured zone and con-equently, the fractures tends to open. In this stage, the pressure atonitoring Point 2 increases straightly till the entire fractured zone

re fractured. When the fractured zone begins to leakage, a sud-en pressure drop at Monitoring Point 2 is observed because of theonnection between the saline layer and aquifer layer. Meanwhile,he fluxes will also decrease with the drop of pressure because theffective stress increases.

In addition, there is a sudden pressure drop in the pressureurves at Monitoring Point 1, as shown in Figs. 12 and 13. Thiseculiar phenomenon is the signal of CO2 infusion into fracturedones, as shown in Fig. 14. The beginning of pressure drop indi-ates that supercritical CO2 is starting to invade the fractured zone.

hen the CO2 fully penetrates the caprock along the fractured zone,he pressure increases again as shown in Fig. 14b. There are severalontributing factors: (1) the relative permeability for CO2 fluid flowncreases as the entire fractured zone are saturated with CO2; (2)upercritical CO2 is much less viscous than the brine and water, andts mobility increases when fractured zone is saturated with CO2;3) when CO2 fully penetrate the fractured zone, the high-pressureayer and low-pressure layer are communicated with each other,nd this result in the pressure drop in the fractured zone.

Fig. 15 shows the influence of different injection rates on theressure changes. Results show similar trends for different injec-ion rates except for the relative lower rate 0.01 kg/s. Fluid-drivenracturing will not take place with such relative lower injectionate (the blue line). From the simulation results, the times of initialracturing with different injection rates are 74 days, 102 days, and10 days, respectively. In addition, the pressure increases shown inig. 15 are different for different injection rates.

.4. Influence of different parameters of fractured zones

In this section, we will further investigate the influence of dif-erent parameters for hydraulic fractured zones on the pressureesponse, including the initial hydraulic fracturing permeability,

he location, and the amount of fractured zones. For simplicity,ll the model properties in the following numerical simulationsre same as the simulations in Section 5.3. Here, the injection

Fig. 15. Pressure changes in the Monitoring Point 1 with different injection rates.

Z.-Q. Huang et al. / International Journal of Greenhouse Gas Control 34 (2015) 39–51 49

(a) Monitoring Point 1 (b) Monitoring Point 2

0

300

600

900

1200

1500

1800

0 400 800 1200 1600 2000

Pres

sure

incr

ease

(kPa

)

Time (days)

k0=10 Dk0=0.1 Dk0=10 mDno fractu re

0

550

1100

1650

2200

2750

3300

0 400 800 1200 1600 2000

Pres

sure

incr

ease

(kPa

)

Time (days)

k0=10 Dk0=0.1 Dk0=10 mDno fractu re

F ulic frl

rx

paPutmi

phdsfspmflTc

t

ig. 16. Pore pressure changes at the monitoring points with different initial hydraegend, the reader is referred to the web version of this article.)

ate is constant, i.e. 0.07 kg/s, and the fractured zone is located at = 4305 m.

(1) Influence of initial fracture permeabilityFig. 16 shows the influence of initial fracture permeability on

ressure changes. Although the initial hydraulic fracturing perme-bility differs, the initial fracturing time is the same. For Monitoringoint 1, the results show the similar trends for pressure changessing different injection rates (as depicted in Fig. 14). However,here are some differences for Monitoring Point 2. In principle, the

agnitude of pressure increase trends to decrease with increasingn initial fracture permeability.

As shown in Fig. 16b, there are three distinct stages for theseressure changes. In Stage 1, before fracturing, the pressure downole increases quickly due to the CO2 injection. In this stage, CO2isplaces the saline and transports to the upper layer, the pore pres-ure increases noticeably in a short time. When the fluid-drivenracturing occurs, in the Stage 2, the pressure increases relativelowly. After CO2 fully penetrates the caprock, Stage 3 starts andressure decreases gradually. Moreover, for a relative larger per-eability (kf0 = 10 D), the pressure may decrease suddenly when

uid-driven fracturing begins, as shown in Fig. 16b (green line).hese characteristics can be helpful to identify the fracturing of

aprocks.

(2) Influence of the location of a fractured zoneThe current study also investigates the influence of fracture loca-

ions on the pressure response. Three scenarios of a fractured zone

(a) Moni toring P oin t 1

0

300

600

900

1200

1500

1800

0 400 800 1200 1600 2000

Pres

sure

incr

ease

(kPa

)

Time (days)

d=0 md=300 md=500 mno fractu re

Fig. 17. Pore pressure changes at the monitoring points w

acturing permeabilities. (For interpretation of the references to color in this figure

with different distances away from the injection source have beenrun. Fig. 17 shows the pressure responses at two Monitoring Points.

It is observed that the farther the fractured zone is from theinjection source, the smaller the magnitude of pressure signals arereduced. Therefore, the variation in pore pressure response at themonitoring points could be helpful to determine the location offracture zones in the caprock. Meanwhile, we can find that the ini-tial fracturing times are little different between different locations.However, the time of CO2 fluid arrived at fracture zones are verydifferent. This is because the transient pressure transient transmitmore quickly than the mass components. So it is better to use apressure signal other than a fluid phase monitor to identify theexistence of fractures in the caprock.

(3) Influence of the distribution of fractured zonesIn order to investigate the influence of the numbers of fracture

zones, three scenarios are run in this section. The first scenario onlyincludes one fracture zone which locates at x = 4105 m. The sec-ond scenario contains two fracture zones which are at x = 4105 mand 4305 m, respectively. The third scenario contains three fracturezones which are at x = 4105 m, 4305 m, and 4505 m, respectively.And the properties of these fracture zones are same as the examplein Section 5.3.

Fig. 18 shows the pressure response at two Monitoring Points.It was observed that the initial fracturing times are the same andthe times of CO2 fluid invaded into fracture zones are also thesame. This is because the pressure signal is dependent on the closer

(b) Moni torin g P oin t 2

0

550

1100

1650

2200

2750

3300

0 400 800 1200 1600 2000

Pres

sure

incr

ease

(kPa

)

Time (days)

d=0 md=300 md=500 mno fractu re

ith different distances away from injection source.

50 Z.-Q. Huang et al. / International Journal of Greenhouse Gas Control 34 (2015) 39–51

Monitorin g P oin t 1 Moni torin g P oin t 2

0

400

800

1200

1600

2000

0 400 800 1200 1600 2000

Pres

sure

incr

ease

(kPa

)

one fractu red zonetwo fr actur ed zon esthree fractured zonesno fractu re

0

550

1100

1650

2200

2750

3300

0 400 800 1200 1600 2000

Pres

sure

incr

ease

(kPa

)

one fractu red zonetwo fr actur ed zon esthree fractured zonesno fractu re

ng poi

fcab

6

TmTncedcppfef

(

(

(

Time (days)

Fig. 18. Pore pressure changes at the monitori

racture zone. With the increase in numbers, the pressure increaseurves are more coincident, and the magnitudes of pressure signalre increased at Monitoring Point 2. The opposite phenomena cane found at Monitoring Point 1.

. Conclusions

In this work, an efficient parallel fully-implicit simulator, namedHM-CO2, has been developed to couple thermal, hydraulic andechanical (THM) processes in geological media for CO2 storage.

he validity of the numerical model is verified by comparison ofumerical results with the analytical solutions of two classicalonsolidation problems. Based on THM-CO2, a set of numericalxperiments have been run to investigate the fluid flow behavioruring CO2 injection, especially for CO2 leakage through geome-hanically caprock fractures or activated faults. In this paper, weropose an implicit and simplified model to simulate the fractureropagation by using some practical correlations (e.g. hydraulicracturing pressure functions, permeability–stress relationships,tc.) rather than explicit simulation. The main conclusions drawnrom this study are as follows:

1) If a vertical pathway is available or created due to the pres-sure buildup during CO2 injection, CO2 tends to flow upwardand escape, and may reach to the upper aquifer layer. The sim-ulation results indicate that the transient pressure responsecan be detected by using permanent downhole gauges (PDGs).Meanwhile, the results show that there are strong correlationsbetween the monitoring pressures and CO2 leakage flux fromthe fractured zone. At the beginning of fluid-driven fracturing,the pressure of PDGs in aquifer layer will increase suddenly,and the pressure increase trend will slow down or suddenlydrop with continual injection. These transient pressure signalsenable us to identify the existence of fractures in caprock.

2) The injection rate is the major factor for fluid-driven fractur-ing in caprock. It is directly determine the initial fracturingtime. The simulation results suggested that slowly increasingthe injection rate at the beginning of CO2 injection may reducepossibility of caprock damage. There should be a critical injec-tion rate to fracture caprock. In this study, the critical injectionrate is between 0.01 kg/s and 0.015 kg/s.

3) The numerical results show that similar trends of pressure

increase at PDGs are found with different parameters of frac-tured zone, such as location, initial fracture permeability andthe amount of fractured zones. Specifically, these indicate thatit is possible to develop a technical approach by integrating

Time (days)

nts with different numbers of fractured zones.

in-situ pressure data, measured from PDGs of multiple wells,into modeling analysis using the THM-CO2 simulator developedfor CO2 storage in reservoirs, to quantify the potential leakagepathways as well as leaking rates.

Acknowledgements

This work was supported by the CMG Foundation, the NationalNatural Science Foundation of China (Grant nos. 51404292,51234007), Natural Science Foundation of Shandong Province ofChina (ZR2014EEQ010), and the Fundamental Research Fundsfor the Central Universities of China (13CX05007A, 13CX02052A,14CX05027A, 14CX06091A).

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